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Traveling wave solutions of nonlinear evolution equations via the F-expansion method | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 آبان 1404 اصل مقاله (18.74 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66357.3092 | ||
| نویسندگان | ||
| Salim Saeed Mahmood* 1؛ Muhammad Amin Sadiq Murad2؛ Shilan Sofe Omer3؛ Shaima Sofe Omer3؛ Shaima Jamel Saeed3 | ||
| 1Department of Mathematics, Faculty of Science, Soran University, Erbil, Iraq. | ||
| 2Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq. | ||
| 3Department of Mathematics, Faculty of Education, Soran University, Erbil, Iraq. | ||
| چکیده | ||
| In this study, we investigate the analytical solutions of three fundamental nonlinear evolution equations: the Korteweg-de Vries (KdV) equation, the modified Korteweg-de Vries (mKdV) equation, and the variant Boussinesq equations using the F-expansion method. Despite extensive research on these equations, significant gaps remain in understanding their complete solution structures and dynamic behaviors under various parametric conditions. By applying the F-expansion technique combined with traveling wave transformations, we derive multiple families of exact analytical solutions exhibiting diverse wave phenomena. The solutions are comprehensively visualized through 2D and 3D graphical representations, demonstrating rich wave dynamics and temporal evolution patterns across different parameter regimes. Additionally, we conduct detailed bifurcation analysis using phase portrait techniques and investigate chaotic behaviors through Lyapunov exponent calculations, Poincar'{e} sections, and multistability analysis, revealing complex dynamical structures including equilibrium points and chaotic attractors. The conformable derivative framework is employed to show the influence of fractional parameters on solution behavior. These models are particularly valuable for applications in nonlinear optics, where soliton solutions represent stable pulse propagation in optical fiber communications, plasma physics for ion-acoustic wave phenomena, fluid dynamics for shallow water wave modeling, and wave energy harvesting technologies. The findings contribute to advancing theoretical understanding of nonlinear wave phenomena while providing practical insights for engineering applications in modern optical communication systems and energy conversion technologies. | ||
| کلیدواژهها | ||
| Schrödinger wave equation؛ soliton theory؛ F-expansion method؛ wave solution؛ optical fiber | ||
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